# 1. A little bit of theory

Between 291,000 and 646,000 people worldwide die from seasonal influenza-related respiratory illnesses each year. iF°EVE will change this. iF°EVE will be a life-saver like a defibrillator or a rescue helicopter. First we will take a look at the body core temperature classification:

 Class Body core temperature Hypothermia < 35 °C Normal 36.5-37.5 °C Fever > 38.3 °C Hyperthermia > 40.0 °C Hyperpyrexia > 41.5 °C

Easy to classify depending on the measured temperature only. Next we will take a look at the Naive Bayes classifiers that are commonly used in automatic medical diagnosis. There are many tutorials about the naive Bayes classifier out there, so I keep it short here.

Bayes' theorem:

h: Hypothesis
d: Data
P(h): Probability of hypothesis h before seeing any data d
P(d|h): Probability of the data if the hypothesis h is true

The data evidence is given by

where P(h|d) is the probability of hypothesis h after having seen the data d.

Generally we want the most probable hypothesis given training data. This is the maximum a posteriori hypothesis:

H: Hypothesis set or space

As the denominators P(d) are identical for all hypotheses, hMAP can be simplified:

If our data d has several attributes, the naïve Bayes assumption can be used. Attributes a that describe data instances are conditionally independent given the classification hypothesis:

Every human depending on the age catches a cold 3-15 times a year. Taking the average 9 times a year and assuming a world population of 7· 10^9, we have 63· 10^9 common cold cases a year. Around 5·10^6 people will get the flu per year. Now we can compute:

This means only one of approx. 12500 patients with common cold/flu like symptoms has actually flu! Rests of the data are taken from here. The probability-look-up table for supervised learning looks then as follows:

 Prob Flu Common cold P(h) 0.00008 0.99992 P(Fatigue|h) 0.8 0.225 P(Fever|h) 0.9 0.005 P(Chills|h) 0.9 0.1 P(Sore throat|h) 0.55 0.5 P(Cough|h) 0.9 0.4 P(Headache|h) 0.85 0.25 P(Muscle pain|h) 0.675 0.1 P(Sneezing|h) 0.25 0.9

Therefore:

Note: The probability that an event A is not occurring is given by

Multiplying a lot of probabilities, which are between 0 and 1 by definition, can result in floating-point underflow. Since

it is better to perform all computations by summing logs of probabilities rather than multiplying probabilities. The class with highest final un-normalized log probability score is still the most probable:

# 2. Schematic

Below you will find the initial schematic (right click, view image to enlarge).

Body temperature measurement is done by the infrared thermometer MLX90614ESF-DCA. Temperature...